{"paper":{"title":"An approximate Kappa generator for particle simulations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A q-exponential approximation to the Kappa CDF enables fast inverse-transform sampling of velocities for particle simulations.","cross_cats":["astro-ph.IM","physics.space-ph"],"primary_cat":"physics.plasm-ph","authors_text":"Seiji Zenitani, Takayuki Umeda","submitted_at":"2026-02-05T12:45:04Z","abstract_excerpt":"A random number generator for the Kappa velocity distribution in particle simulations is proposed. Approximating the cumulative distribution function with the q-exponential function, an inverse transform procedure is constructed. The proposed method provides practically accurate results, in particular for k<4. It runs fast on graphics processing units (GPUs). The derivation, numerical validation, and relevance to GPU execution models are discussed."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Approximating the cumulative distribution function with the q-exponential function, an inverse transform procedure is constructed. The proposed method provides practically accurate results, in particular for k<4.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the q-exponential approximation to the Kappa CDF remains sufficiently accurate for the error tolerances required in typical particle-in-cell or Monte-Carlo simulations when kappa is less than 4.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"An approximate inverse-transform sampler for Kappa distributions is constructed via q-exponential CDF fitting and shown to be accurate for kappa less than 4 while running efficiently on GPUs.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A q-exponential approximation to the Kappa CDF enables fast inverse-transform sampling of velocities for particle simulations.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"3f459a6329dcae8a0df87c82b5c91761c725b26813ebf02d2932b7f31c611af9"},"source":{"id":"2602.05606","kind":"arxiv","version":3},"verdict":{"id":"1672513d-4273-4422-a704-bd360311e500","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T07:05:22.225102Z","strongest_claim":"Approximating the cumulative distribution function with the q-exponential function, an inverse transform procedure is constructed. The proposed method provides practically accurate results, in particular for k<4.","one_line_summary":"An approximate inverse-transform sampler for Kappa distributions is constructed via q-exponential CDF fitting and shown to be accurate for kappa less than 4 while running efficiently on GPUs.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the q-exponential approximation to the Kappa CDF remains sufficiently accurate for the error tolerances required in typical particle-in-cell or Monte-Carlo simulations when kappa is less than 4.","pith_extraction_headline":"A q-exponential approximation to the Kappa CDF enables fast inverse-transform sampling of velocities for particle simulations."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2602.05606/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"23657cfd36ce398a114c10d2b04d6b74ad5f412c65a5e22a3504310a5f73465a"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}